Explanation

(b)
$0.0373737\ldots = 0.037 + 0.00037 + 0.0000037 + ...$
$= \frac{37}{10^{3}} + \frac{37}{10^{5}} + \frac{37}{10^{7}} + ...$
$= \frac{37}{10^{3}}\left\lbrack 1 + \frac{1}{100} + \frac{1}{10000} + ... \right\rbrack$
$= \frac{37}{10^{3}}\left( \frac{1}{1 - \frac{1}{100}} \right) = \frac{37}{990}$
Alternate Given value is of the form
[image:9_image5.emf]
[image:9_image6.emf]
$= \frac{037 - 0}{990} = \frac{37}{990}$